GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 25 Mar 2019, 21:19

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53831
If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

New post 26 Nov 2018, 01:25
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:23) correct 33% (01:49) wrong based on 126 sessions

HideShow timer Statistics

Manager
Manager
User avatar
S
Joined: 19 Nov 2017
Posts: 177
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

New post 26 Nov 2018, 01:39
1
Bunuel wrote:
If x, y and z are positive numbers, is \(\frac{x}{y} > \frac{x + z}{y + z}\) ?


(1) x > z

(2) x > y


\(\frac{x}{y} > \frac{x + z}{y + z}\)
Cross multiplying
xy + xz > xy + yz
xy + xz > xy + yz
x>y

Hence, B
_________________
Regards,

Vaibhav



Sky is the limit. 800 is the limit.

~GMAC
SVP
SVP
User avatar
P
Joined: 18 Aug 2017
Posts: 2497
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

New post 26 Nov 2018, 18:34
Bunuel wrote:
If x, y and z are positive numbers, is \(\frac{x}{y} > \frac{x + z}{y + z}\) ?


(1) x > z

(2) x > y


From given eqn we can deduce the following:
xy+xz>xy+yz
z(x-y)>0--(A)

so using 1: x>z , we are not given any relation about y so in -sufficient

From 1: X>Y
for any value of X >Y value the equation ( A) would stand true so B is sufficient..
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53831
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

New post 24 Dec 2018, 01:45
Intern
Intern
avatar
B
Joined: 24 Dec 2018
Posts: 40
Location: India
If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

New post 29 Dec 2018, 04:47
1
There are two methods to solve this question.

Method 1:

Since x, y, z are all positive numbers, we can easily carry their denominators over the inequality without the fear of messing with the inequality.

Hence, \(\frac{x}{y} > \frac{x + z}{y + z}\) can be written as x(y+z)>y(x+z)
This implies xy+xz>xy+yz

Again, xy is a positive number here, so we cancel it out from both sides, leaving us with xz>yz. Taking the expression to one side of inequality, we get xz-yz>0

Thus, either z>0 and x>y or z<0 and x<y.

Now, we are given that z>0 (its a positive number). Hence, for the expression to be definitely true, we must also get x>y. And statement 2 does that for us.

Hence statement 2 is sufficient


Method 2:

Now, if we add the same positive number z to x and y in the fraction x/y, \(\frac{x + z}{y + z}\) will come closer to 1.

This gives us two possibilities:

1) If x/y<1, then \(\frac{(x+z)}{(y+z)}\) is greater than x/y

and

2) If x/y>1, then \(\frac{(x+z)}{(y+z)}\) is smaller than x/y

In our case, 2) works and this is satisfied only by statement 2. Hence, sufficient

Answer is B

Note: For anyone looking for more explanation on concept I used in statement 2, there is an article I think written by Karishma somewhere on GMATclub explaining this. If interested, I can look it up.
_________________
Hit Kudos if you like my answer!
Intern
Intern
avatar
B
Joined: 11 Feb 2019
Posts: 5
Location: United Arab Emirates
GMAT ToolKit User
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

New post 26 Feb 2019, 01:37
For x/y to be greater, x/y needs to be greater than 1 or x>y

S1 irrelevant
S2 x>y hence a definitive Yes -> sufficient
GMAT Club Bot
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?   [#permalink] 26 Feb 2019, 01:37
Display posts from previous: Sort by

If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.